The description of Lord shiva is holder of Trishul and damaru, holder of pinaka bow, Ganga flowing from his head, having a moon on head, having snake in his neck,having 3 eyes,having body covered by ashes, his wife Parvati mata and his sons Ganesha and Kartikeya,wearing animal skin.usually this is the description of Shiva so is this same description found in Vedas as I heard his description is different in Vedas and different in Puranas.
।। Shiva in Vedas ।। vs ।। Shiva in Puranas।।
First of all I would like to suggest to read this post:
It's because citing the same thing here would make answer extremely long. In it you can already see attributes like Nilagriva (blue necked one), Tryambakam (Three eyed one), Kapardin (Who has matted hair), etc...
Similarly Lord Shiva is Tripurantaka as described in Vedas:
Similarly Lord Shiva is also destroyer of Yajna (Makhantaka):
It's also told in Gopatha Brahamana of AtharvaVeda.
Lord Shiva also lives in Kailasha as told in RigVeda:
कैलासशिखरे रम्ये शंकरस्य शुभे गृहे ।
देवतास्तत्र मोदन्ति तन्मे मनः शिवसंकल्पमस्तु ।।
On the charming peak of Kailasha mountain is the home temple of the Peace-creator Shiva; gods rejoice in that. May such my mind be of beautiful and divine resolves, filled with Shiva-thoughts.
He takes Eight forms and becomes all this universe:
He punishes Lord Prajapati also.
Above all links contains the required references for the below finalised points:
1) Names of Shiva:
Suppose that I want to say that I know only Vedas and I want to chant Lord Shivas name as described in Vedas only, I would chant as:
Shiva, Shankara, Nilalohita, Ishana, Bhava, Rudra, Sarva, Pashupati, Ugra, Nilagriva, Sitikantha, Pinakapani, Krritivasa, Tryambaka, Kapardin, Hara, Mahadeva, Maheswara, Sadyojata, Vamadeva, Tatpurusha, Aghora, Sahasraksha, Vyuptakesha... etc..
A reader of Puranas will also chant all the above names along with additional names like:
Gangadhara, Chandrashekhara, etc...
2) Form of Shiva:
Suppose that I want to say that I know only Vedas and I want to meditate upon Lord Shiva as described in Vedas only, I would meditate as:
Along with his consort Uma (Umapati) I meditate upon Shiva who is three eyed (Tryambakam), who has matted hair (Kapardin), who is riding in bull (Vabhlusaaya bi vyadhine), who has blue neck (Nilagriva), who is holding Pinaka bow (Pinakam vibhradaagahi), who wears animal hide (Krittivasa), who is bright as gold, who lives in Kailash Mountain (Kailasha Shikhara Rammye) ....
And the reader of Puranas will also tell the exact above description with few additions like:
who wears Ganga on his head, snakes on his neck.
So, it's not that form of Shiva of Vedas and form of Shiva of Puranas are different, It's only that Puranas contains additional forms.
3) Deeds of Shiva:
Reader of Vedas only would describe deeds of Shiva as:
He who took the Eight forms and became the world (AshtaMurti), He who destroyed the Tripuras making Gods as bows, arrows and chariots (Tripurantaka), who is the destroyer of sacrifice (Makhantak), who punished Prajapati, who is present as form of Lord Agni..
Reader of Puranas will also recall the above all deeds along with many additional deeds like:
manifestation in various Jyotirlingas, Kirata form, helping Ashwatthama etc...
4) Shiva Tatwam:
Reader of Veda only would describe Shiva Tatwam as:
Lord Shiva is the one who is one without second (Eko Hi Rudro Na Dwitiyaya), who himself becomes the eight (AshtaMurti), who is Antaryami of everything, who saw Hiranyagarbha being born, who himself is everything of universe (Sri Rudram), who is Lord of all things (Pashunam Pati, Anna Pati, Jagat Pati, Bhuta Pati, Kshetra Pati etc.. of Sri Rudram), who is all (Sarvo Vai Rudras tasmai)....
Reader of Puranas will also recall all the above philosophy along with some additional details like:
concept of 36 Tatwas, kãla nirnaya etc.. and so on.
5) Worship of Shiva:
A reader of Vedas would worship Lord Shiva as:
Doing Homam of Sri Rudram, Japam of names of Sri Rudram, Chanting Panchakshara Mantra (Namaha Shivaya), chanting of Tryambakam and PanchaBrahman mantras, remembering of Linga form, Pashupata Vrata, Surrender, etc...
Reader of Puranas would also worship Lord Shiva in the above way with some additional details like:
chanting Shiva Sahasranama, chanting various stotras etc...
Thus it's only that Puranas contain additional information. It is not necessary that Vedas would make every reference, Vedas only make eternal references.
Some descriptions of Lord Shiva which are found in the later-day scriptures are found in the Vedas too. But not all the known features are found.
Lord Shiva's consort Goddess UmA:
Namah somAya cha rudrAya cha.
Salutation to Soma, and to Rudra.
Soma: One with Uma (sa+uma)
Tattiriya SamhitA 4.5.8
Lord Shiva being white-complexioned:
Lord Shiva is extremely fair; his complexion is like that of camphor or snow or that of milk. In Vedas too he is mentioned as Vilohita meaning white.
Vikirida vilohita namste astu bhagavah.
O scatterer of riches (vikrid), who is white (vilohita), salutation to you, O Bhagavan.
Lord Shiva's weapons-the Trishula and the PinAka bow; Lord Shiva wearing tiger skin.
The following mantra alludes to the Trishula and the PinAka bow, without directly naming them. The very next given mantra mentions the name of the Bow explicitly.
Namah svAyudhAya cha sudhanvane cha.
Salutation to him of the auspicious weapon (trishulA), and to him of the auspicious bow (pinAka).
Parame vriksha Ayudham nidhAya krittim vasAna A chara, PinAkam bibhrad Agahi.
Placing down your weapon on the highest tree, clad in your tiger skin, come, and approach us bearing the spear (bow) PinAka.
Lord Shiva as the Three-eyed Lord:
Trayambaka means three-eyed. But it also means the Lord of the three worlds, as is found in the next given famous MahAmrityunjaya mantra from Rig Veda. The translation is as per the Sri Aurobindo-Sri KApaly ShAstry school.
Trayambakam yajAmahe sugandhim pushti vardhanam
UrvArukam iva bandhanAn mrtyor mukshiya mA amrtat ||
We adore the Father of the three worlds, Trayambaka, bestower of all sided fragrance of grace, increaser of fullness and strength; May i be detached from the bondage of death like a ripe cucumber from the stem, but not from immoratality.
Rig Veda 7.59.12
Lord Shiva living in the KailAsha mountain:
At many places it is mentioned, in the famous Sri Rudram from the Yajur Veda, that Lord Shiva resides in Giri or mountain. I am not sure though, whether any where in the Vedas, the exact name KailAsha is found or not.
Namo girishAya cha shipivishtaya cha.
Salutation to him who resides in the mountains and to ShipivishtA (one who is pervaded by rays of knowledge).
Tattriya SamhitA 4.5.5
Note- Some of the above mantras are Riks from Rig Veda and some are Yajus from Yajur Veda. .
Many descriptions of Lord shiva are found in the Vedas like
Living in kailash
कैलासशिखरे रम्ये शंकरस्य शुभे गृहे । देवतास्तत्र मोदन्ति तन्मे मनः शिवसंकल्पमस्तु ।। 24
In the summit of Kailash is the beautiful home of Shankara. Gods rejoice in that, May my mind be filled with Shiva thoughts.(Rig Veda khillani sukta shiva sankalpla sukta verse 24)
Note-this is not found in the Rig Veda but in The khillani suktas of Rigveda which are associated with baskala shaka of Rig Veda.
Devi uma being wife of shiva
म्बिका पतय उमापतये पशुपतये नमः।
Salutations and Salutations to Ambikapati (Lord of Ambika), Umapati (Lord of Uma) and Pasupati.(taitterya Aryanaka 10.22.1)
Having Lord ganesha and Kartikey his son
तत्पुरुषाय विद्महे वक्रतुन्डाय धीमहि तन्नो दन्ति प्रचोदयात् । We meditate upon Him who has a curved trunk. May the tusked One guide us on the right path.(taitterya aryanaka of yajurveda 10.1.5)
तत्पुरुषाय विद्महे महासेनाय धीमहि तन्नो षण्मुख प्रचोदयात् ।
We meditate upon Him who is great commander , may Shanmukha ( Kumara) guide us on right path.(taitterya aryanaka of yajurveda 10.1.6)
Holding pinaka bow,Trishula has already mentioned in rickross answer